Synthetic aperture radar (SAR) imaging provides a method for increasing the resolution of small and low-cost frequency-modulated continuous-wave multiple-input multiple-output radar sensors. SAR images provide a dense representation of the environment, which may be used for scan matching in a simultaneous localization and mapping (SLAM) system. This article presents the details of an indoor SLAM system that utilizes SAR images for loop closure detection and scan matching. The obtained trajectory accuracy is compared against a laboratory reference system, and SAR imaging results are presented.